Evaluations of Coupled Transverse-Rotational Galloping of Slender Structures with Nonlinear Effect

This paper presents evaluations of coupled two-degree-of-freedom (2DOF) galloping oscillations of slender structures with nonlinear effects, involving coupled transverse and rotational motions. The nonlinear governing equations of the coupled motions are derived by developing nonlinear formulations of the quasi-steady aerodynamic forces and damping coefficients. By solving the eigenvalue problem of a perfectly tuned 2DOF system, an analytical expression of the minimal structural damping ratio required to prevent coupled transverse-rotational galloping is established. The influences of various parameters, such as angle of wind attack, structural height, width and aspect ratio, on the onset wind velocity for the occurrence of coupled galloping are then analyzed in detail by numerical simulations. Comparisons of the onset wind velocity of the coupled 2DOF and uncoupled single-degree-of-freedom (1DOF) galloping are presented and discussed. The nonlinear vibration behavior of coupled 2DOF galloping of slender structures under varying wind speeds is also investigated.